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Fractions and decimal numbers

A fraction is one number divided by another number. There are several ways to write a number divided by another one, such as a ÷ b , a / b and a b . The first way of writing a fraction is very hard to work with, so we will useonly the other two. We call the number on the top (left) the numerator and the number on the bottom (right) the denominator . For example, in the fraction 1 / 5 or 1 5 , the numerator is 1 and the denominator is 5.

Definition - fraction

The word fraction means part of a whole .

The reciprocal of a fraction is the fraction turned upside down, in other words the numerator becomes the denominator and the denominator becomesthe numerator. So, the reciprocal of 2 3 is 3 2 .

A fraction multiplied by its reciprocal is always equal to 1 and can be written

a b × b a = 1

This is because dividing by a number is the same as multiplying by its reciprocal.

Definition - multiplicative inverse

The reciprocal of a number is also known as the multiplicative inverse.

A decimal number is a number which has an integer part and a fractional part. The integer and the fractional parts are separated by a decimal point , which is written as a comma in South African schools. For example the number 3 14 100 can be written much more neatly as 3 , 14 .

All real numbers can be written as a decimal number. However, some numbers would take a huge amount of paper (and ink) to write out in full! Some decimal numberswill have a number which will repeat itself, such as 0 , 33333 ... where there are an infinite number of 3's. We can write this decimal value by using a dotabove the repeating number, so 0 , 3 ˙ = 0 , 33333 ... . If there are two repeating numbers such as 0 , 121212 ... then you can place dots or a bar, like 0 , 12 ¯ on each of the repeated numbers 0 , 1 ˙ 2 ˙ = 0 , 121212 ... . These kinds of repeating decimals are called recurring decimals .

[link] lists some common fractions and their decimal forms.

Some common fractions and their equivalent decimal forms.
Fraction Decimal Form
1 20 0,05
1 16 0,0625
1 10 0,1
1 8 0,125
1 6 0 , 16 6 ˙
1 5 0,2
1 2 0,5
3 4 0,75

Scientific notation

In science one often needs to work with very large or very small numbers. These can be written more easily in scientific notation, which has the general form

a × 10 m

where a is a decimal number between 0 and 10 that is rounded off to a few decimal places. The m is an integer and if it is positive it represents how many zeros should appear to the right of a . If m is negative, then it represents how many times the decimal place in a should be moved to the left. For example 3 , 2 × 10 3 represents 32 000 and 3 , 2 × 10 - 3 represents 0 , 0032 .

If a number must be converted into scientific notation, we need to work out how many times the number must be multiplied or divided by 10 to make it into anumber between 1 and 10 (i.e. we need to work out the value of the exponent m ) and what this number is (the value of a ). We do this by counting the number of decimal places the decimal point must move.

For example, write the speed of light which is 299 792 458 m · s - 1 in scientific notation, to two decimal places. First, determine where the decimalpoint must go for two decimal places (to find a ) and then count how many places there are after the decimal point to determine m .

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: grade 10 maths [caps]. OpenStax CNX. Aug 03, 2011 Download for free at http://cnx.org/content/col11306/1.4
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